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Disability Insurance Loss Probability Calculator

This calculator compounds a user-entered annual disability probability into the probability of at least one modeled disability event over several years. It is a pure probability tool and does not estimate whether a specific person will qualify for benefits under an insurance policy.

The model holds annual probability constant and treats yearly events as independent. That makes it useful for sensitivity analysis, while also making clear why it should not be mistaken for an underwriting or actuarial forecast.

Convert annual disability risk to a multi-year probability

%
years
Result
—
Cumulative probability of at least one modeled disability event
No-event probability—
Annual probability—
Analysis horizon—

1. Enter an annual probability
Use a rate from a source or assumption suitable for your scenario.

2. Choose the number of years
Enter the horizon over which the same annual probability will be repeated.

3. Review cumulative risk
The main result is the probability of one or more modeled events during the horizon.

4. Compare the no-event probability
The complementary result shows the chance of going through the entire horizon without the modeled event.

5. Test alternative assumptions
Change the annual rate or years to see how cumulative probability responds.

No-event probability = (1 − Annual probability)^Years Cumulative disability probability = 1 − No-event probability

The annual rate is converted from a percentage to a decimal. The formula assumes the same independent annual probability every year and does not model recovery, recurrent disability, occupation changes, or aging.

What the result means

The result is the modeled chance of at least one disability event over the chosen horizon under a constant annual probability.

Insurance coverage depends on the policy definition of disability and other terms; a modeled event is not automatically a payable claim.

Given: Annual disability probability = 3%; horizon = 10 years.

Calculation: No-event probability = (1 − 0.03)^10 = 0.7374, or 73.74%. Cumulative probability = 1 − 0.7374 = 0.2626.

Result: Cumulative modeled disability probability ≈ 26.26%.

Interpretation: Repeating a 3% annual probability over ten years produces a cumulative probability greater than 3%, while still remaining below simple 3% × 10 because probabilities compound.

Why does cumulative probability not equal annual probability times years?

The complement formula accounts for the possibility of avoiding the event in each successive year. Simple multiplication is only an approximation at very low probabilities and short horizons.

Can I use an occupational disability statistic as the annual input?

You can if it is suitable for your purpose, but make sure its definition and population match the scenario. Different sources may define disability differently.

Does the calculator allow more than one disability event?

It only calculates the probability of at least one event. It does not count repeat claims or recurrent disabilities.

Does this tell me whether a policy will pay?

No. A payable claim depends on the contract definition of disability, elimination period, exclusions, proof requirements, and other terms.

What is the main limitation of the model?

It assumes a constant independent annual probability, while real disability risk can change with age, occupation, health, and other conditions.